On tangential star products for the coadjoint Poisson structure

Star Products on Coadjoint Orbits

A Comparison Between Star Products on Regular Orbits of Compact Lie Groups

In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. Investigation supported by the Universi...

فرمولبندی هندسی کوانتش تغییرشکل برزین

  In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...

On Generalized Abelian Deformations

We study sun-products on R, i.e. generalized Abelian deformations associated with star-products for general Poisson structures on R. We show that their cochains are given by differential operators. As a consequence, the weak triviality of sun-products is established and we show that strong equivalence classes are quite small. When the Poisson structure is linear (i.e., on the dual of a Lie alge...

Hamiltonian Systems with Symmetry, Coadjoint Orbits and Plasma Physics

The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the Lie-Poisson structure on the dual of a Lie algebra. These results are applied to plasma physics. We show in three steps how the Maxwell-Vlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisso...